On Wed, Feb 16, 2005 at 12:17:35PM +1100, Damian Conway wrote:
> Rod Adams wrote:
> >On a slightly different topic, do the following equivalences work:
> >[...]
> >none($a, $a) == undef
> True.
Scott already caught (and Damian acknowledged) this one, it's false
if $a == undef.
> >none($a,$a,$b) == none($a,$b)
> True.
Okay, I follow this one -- here's the derivation.
-> none($a == none($a, $b),
$b == none($a, $b))
-> none(none($a==$a, $a==$b),
none($b==$a, $b==$b))
-> none(none(1, 0), none(0, 1))
-> none(0, 0)
-> true
> >none(none($a,$b),none($c,$d)) == none($a,$b,$c,$d)
> True.
Hmmmm...
-> none(none($a,$b) == none($a,$b,$c,$d),
none($c,$d) == none($a,$b,$c,$d))
-> none(none($a == none($a,$b,$c,$d),
$b == none($a,$b,$c,$d)),
none($c == none($a,$b,$c,$d),
$d == none($a,$b,$c,$d)))
-> none(none(none($a==$a, $a==$b, $a==$c, $a==$d),
none($b==$a, $b==$b, $b==$c, $b==$d)),
none(none($c==$a, $c==$b, $c==$c, $c==$d),
none($d==$a, $d==$b, $d==$c, $d==$d)))
-> none(none(none(1, 0, 0, 0),
none(0, 1, 0, 0)),
none(none(0, 0, 1, 0),
none(0, 0, 0, 1)))
-> none(none(0, 0), none(0, 0))
-> none(1,1)
-> false
Ummm, what am I missing? To state it another way... we can
show that none($a,$b) == none($a, $b, $c, $d) is true, so
none( none($a,$b), none($c,$d) ) == none($a, $b, $c, $d)
is equivalent to
none( none($a,$b) == none($a, $b, $c, $d),
none($c,$d) == none($a, $b, $c, $d))
which is none(1, 1), or false. Did I autothread wrongly here?
And for completeness...
> >one($a,$a,$b) == ($a == $b ?? undef :: $b)
> True.
...except when $a == $b == undef.
Pm
